Question

Let S be the set of first 18 natural numbers. Find the number of ways selecting 3 numbers such that they are all consecutive.

Answer 1

Hint: We first find the trick to form the consecutive three numbers. We try to find the middle number from the stack of numbers of $1,2,...,18$. We omit 1 and 18 and then find the number of ways as the solution.

Complete step-by-step answer:
We have to find the number of ways we can select 3 numbers from the set of first 18 natural numbers.
We will try to use the middle number of the set of 3 numbers. The set will be of consecutive numbers only if the middle number satisfies the condition.
The first 18 natural numbers are $1,2,...,18$. We have to choose a number for the middle number of the 3 numbers’ set.
We can’t take 1 and 18 as the middle number as then we won’t be able to find the other two numbers as they are the previous and the following number.
So, we are choosing a number for the middle number from the range of $2,...,17$.
The number of choices is 16.
So, the correct answer is “16”.

Note: We can also solve the problem in the form of taking the first or last number instead of taking the middle number. The process and the solution remain the same for both cases.